System and Method For Determining Intermodulation Distortion In A Radio Frequency

ABSTRACT

The present disclosure describes systems and methods for identifying a signal that is a product of two or more other signals. In an embodiment, the presence of intermodulation distortion in a communication system is determined by comparing a cyclic autocorrelation function (“CAF”) of a complex envelop of signal content in a frequency bin, comparing the determined CAF with the CAF for a known signal type, and comparing a frequency of the signal content with the frequency of an RF channel in the communication system.

RELATED AND CO-PENDING APPLICATIONS

This application is a U.S. national stage application of the PCTApplication entitled “System and Method for Determining IntermodulationDistortion In a Radio Frequency Channel”, Serial NumberPCT/US2013/075420 filed 16 Dec. 2013, which claims priority to U.S.provisional application entitled “Cyclostationarity Based Identificationof Intermodulation Distortion”, Ser. No. 61/737,500 filed 14 Dec. 2012.This application is related to each of the following U.S. national stageapplications, each of which is filed concurrently herewith, of thefollowing PCT applications: “System and Method forCyclostationarity-Based Signal Identification”, Serial NumberPCT/US2013/075394, and “System and Method for DeterminingIntermodulation Distortion Of a Radio Frequency Product Signal”, SerialNumber PCT/US2013/075409. The entirety of each of the above applicationsis hereby incorporated herein by reference.

BACKGROUND

Intermodulation distortion is a form of signal distortion caused by anunwanted amplitude modulation of signals that occurs due to passagethrough a non-linear channel. Such intermodulation can cause additionalsignals that are present at various combinations of sums and differencesof the frequencies that constituted the original source signals. Suchintermodulation can cause unwanted signal components to appear in otherfrequency bands and cause interference to other useful signals. Inaddition, this intermodulation can cause signal distortion throughoutthe original band and thus reduce the quality of information-carryingsignal transmissions.

The presence of intermodulation distortion, particularly on the downlinkpath, can be a serious problem for communication network operators. Thisdistortion, which may corrupt existing communication signals and/oroccupy frequency bands that are allocated for other purposes, can causethe communication network to fail to achieve its design throughputcapacity. One known cause of intermodulation distortion is due tocabling and/or connector malfunction or is caused by other passivecomponents. Such intermodulation distortion is referred to herein asPassive Intermodulation Distortion (“PIM”). Unfortunately,intermodulation distortion is not easy to identify without activeinvestigation, such as disconnecting components and subjecting them toscrutiny and/or injecting test signals via sophisticated diagnosticsequipment. Such investigation and testing is costly and time-consumingand requires at least a portion of the communication network to be outof operation for a period of time. Furthermore, cables, connectors, andother passive circuit elements may deteriorate over time due to avariety of reasons including weather and the local operatingenvironment. Thus, for example, cables and connections that check outfine at the time of installation or testing may deteriorate withoutnotice until they cause a decrement in network operation.

Intermodulation distortion is often present in many operationalcommunication networks and the network operator may not be aware untilthe problem becomes large enough that is causes major interference withdata and/or voice carrying communication channels.

Accordingly, there is a need for identifying signals which may be theresult of intermodulation distortion, determining intermodulationdistortion from two or more radio frequency (“RF”) signals, anddetermining intermodulation distortion in a communication system whichoperates using known RF channels and a known communication signal type.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart for identifying a signal according to anembodiment of the present subject matter.

FIG. 2 is a functional block diagram for identifying a signal accordingto an embodiment of the present subject matter.

FIG. 3 is a flow chart for determining intermodulation distortion of aradio frequency product signal according to an embodiment of the presentsubject matter.

FIG. 4 is a functional block diagram for determining intermodulationdistortion of a radio frequency product signal according to anembodiment of the present subject matter.

FIG. 5 is a flow chart for determining radio frequency signals causingintermodulation distortion according to an embodiment of the presentsubject matter.

FIG. 6 is a functional block diagram for determining radio frequencysignals causing intermodulation distortion according to an embodiment ofthe present subject matter.

DETAILED DESCRIPTION

The following description of the present subject matter is provided asan enabling teaching of the present subject matter and its best,currently-known embodiment. Those skilled in the art will recognize thatmany changes can be made to the embodiments described herein while stillobtaining the beneficial results of the present subject matter. It willalso be apparent that for some embodiments, some of the desired benefitsof the present subject matter can be obtained by selecting some of thefeatures of the present subject matter without utilizing other features.Accordingly, those skilled in the art will recognize that manymodifications and adaptations of the present subject matter are possibleand may even be desirable in certain circumstances and are part of thepresent subject matter. Thus, the following description is provided asillustrative of the principles of the present subject matter and not inlimitation thereof and may include modification thereto and permutationsthereof. While the following exemplary discussion of embodiments of thepresent subject matter may be directed towards or reference specificsystems and methods, it is to be understood that the discussion is notintended to limit the scope of the present subject matter in any way andthat the principles presented are equally applicable to other similarsystems and methods for identifying a signal that is a product of two ormore other signals.

Those skilled in the art will further appreciate that many modificationsto the exemplary embodiments described herein are possible withoutdeparting from the spirit and scope of the present subject matter. Thus,the description is not intended and should not be construed to belimited to the examples given but should be granted the full breadth ofprotection afforded by the appended claims and equivalents thereto.

With reference to the figures where like elements have been given likenumerical designations to facilitate an understanding of the presentsubject matter, various embodiments of a system and method foridentifying signals which may be the result of intermodulationdistortion, determining intermodulation distortion from two or moreradio frequency (“RF”) signals, and determining intermodulationdistortion in a communication system which operates using known RFchannels and a known communication signal type, are described. In anembodiment, the presence of a particular signal is determined andidentified by applying a cyclostationarity detection technique. One suchtechnique includes comparing a cyclic autocorrelation function of aproduct signal with the cyclic autocorrelation function of at least oneof the signals which formed the product signal. In another embodiment,intermodulation distortion is determined by searching a frequency bandfor an RF product signal and identifying the RF product signal as anintermodulation distortion signal using a cyclostationarity detectiontechnique. In a further embodiment, the presence of intermodulationdistortion in a communication system is determined by comparing a cyclicautocorrelation function (“CAF”) of a complex envelop of signal contentin a frequency bin, comparing the determined CAF with the CAF for aknown signal type, and comparing a frequency of the signal content withthe frequency of an RF channel in the communication system. In yet afurther embodiment, the presence of intermodulation distortion or otherforms of interference in a communication system is determined throughcyclostationary Spectral Correlation Density (“SCD”). The SCD is used tofurther evaluate the nature of the interfering signal, such as spectralenergy, modulation type, etc. The SCD may be determined by a FrequencySmoothing and/or Time Smoothing algorithm.

The disclosed systems and methods may be used to identifyintermodulation distortion, including passive intermodulation distortionin a system such as, but not limited to, a communication systemincluding a wired or a wireless communication system. In an embodiment,the techniques include classifying a signal or signals according totheir cyclostationary properties. Intermodulation distortion isidentified by searching for cyclostationary properties of the productwaveforms generated due to the underlying distorting process. One ormore regions of signal spectrum may be sequentially examined for productwaveforms with such properties. By applying certain hypotheses tests,the likelihood of intermodulation distortion is determined. The systemsand methods may be applied to any digital signal type.

Passive intermodulation distortion is a form of signal distortion causedby an unwanted amplitude modulation of signals that occurs due to theirpassage through a non-linear channel and caused by passive components.Such intermodulation can cause additional, generally undesirable signalsto be generated at various combinations of sums and differences of thefrequencies that constituted the original source signal. It can thuscause unwanted signal components to appear in other frequency bands andcause interference to other signals. In addition, this intermodulationcan cause signal distortion throughout the original band and thus reducethe quality of the transmissions. While the disclosure discussesexamples using PIM, it will be readily understood by those of skill inthe art that the described techniques and procedures are applicable toother types of intermodulation distortion and are not limited to PIM.

Consider a channel within which the desired source signal has frequencycomponents at frequencies

f ₁ ,f ₂ ,f ₃ , . . . f _(N).

Then, on passage through a non-linearity, the output signal hasfrequency components of the form

a ₁ f ₁ +a ₂ f ₂ +a ₃ f ₃ + . . . +a _(N) f _(N)

where the coefficients

a ₁ ,a ₂ , . . . ,a _(N)

are some arbitrary constants. One such case of particular interest iswhere so called third order intermodulation products are formed. This isthe case where the absolute sum of the coefficients of two or more ofthe output signal frequency components equals three. For example:

|a ₁ |+|a ₂ |+|a ₃|=3,

and where spurious signals are now generated at frequencies such as

(f ₁ +f ₂ −f ₃),(2f ₁ −f ₂),(2f ₂ −f ₃).

More generally the absolute sum of the terms a_(i) is referred to as theorder of the intermodulation. Cases where this order is equal to 3, 5,or 7 are the most deleterious, and the third order terms are often thedominant contributors.

For a more detailed understanding of the process giving rise to thesespurious frequency terms, let us consider that we have a channel inwhich we ideally have the signals x₁(t)sin(2πf₁t), x₂(t)sin(2πf₂t),x₃(t) sin(2πf₃t), where x₁(t), x₂(t) and x₃(t) are narrow band signalsrelative to the total channel bandwidth and f₁, f₂, and f₃ arefrequencies such that the signals occur with no overlap within thechannel in the ideal case (the signals are spectrally disjoint). As anexemplary, non-limiting, illustration of the concepts involved, assumethat there is a non-linearity at some point in the signal path whichcubes the entire channel content. It is noted that this is an extremesituation, but useful to illustrate the concepts involved. Moregenerally, the cube typically occurs as one term of a sum of terms inthe channel output. Taking the cube of an expression is a non-linearoperation and the output of the channel is then expressible as

(x ₁(t)sin(270)+x ₂(t)sin(2πf ₂ t)+x ₃(t)sin(2πf ₃ t)³  (1.1)

The expansion of the terms in this equation give rise to the following,terms:

x ₁ ³(t)sin³(2πf ₁ t)+x ₂ ³(t)sin³(2πf ₂ t)+x ₃ ³(t)sin³(2πf ₃ t)+2x ₁²(t)sin²(2πf ₁ t)x ₂(t)sin(2πf ₂ t)+2x ₁ ²(t)sin²(2πf ₁ t)x ₃(t)sin(2πf₃ t)+2x ₂ ²(t)sin²(2πf ₂ t)x ₁(t)sin(2πf ₁ t)+2x ₂ ²(t)sin²(2πf ₂ t)x₃(t)sin(2πf ₃ t)+2x ₃ ²(t)sin²(2πf ₃ t)x ₁(t)sin(2πf ₁ t)+2x ₃²(t)sin²(2πf ₃ t)x ₂(t)sin(2πf ₂ t)+6x ₁(t)sin(2πf ₁ t)x ₂(t)sin(2πf ₂t)x ₃(t)sin(2πf ₃ t)  (1.2)

Now consider the fourth term of this expansion. This is

2x ₁ ²(t)sin²(2πf ₁ t)x ₂(t)sin(2πf ₂ t),

which can be expanded using trigonometric identities as

x ₁ ²(t)x ₂(t)sin(2πf ₂ t)(1−cos(4πf ₁ t)).

This can be further simplified to give

x ₁ ²(t)x ₂(t)sin(2πf ₂ t)−½(x ₁ ²(t)x ₂(t)(sin(2πf ₂ t+4πf ₁ t))−½(x ₁²(t)x ₂(t)sin(2πf ₂ t−4πf ₁ t)  (1.3)

Examining the three terms in equation 1.3, we note that the first termis an interfering signal at the frequency f₂, the third term is a signalat frequency f₂−2f₁ and the second term is a signal at frequency f₂+2f₁.The second term is the most likely to lie outside the frequency bandcontaining the signals, and the second and third are examples where theabsolute sum of the multipliers on the frequency terms is three, asmentioned earlier. We also observe that the signal content for theseterms is the product of the square of one of the original signals andanother original signal. Thus in the case of the second term one signalhas been squared and multiplied by another and the whole product shiftedout to a new frequency of f₂+2f₁. We can also observe that this is onesingle term in the expansion given by equation 1.2. The other terms willproduce similar frequency shifted products of the original signals. Theeffect of intermodulation distortion can thus be interpreted in terms ofthe multiplication of distinct signals having first been raised to smallinteger powers (such as 1, 2, 3, etc.) and various frequency shiftsapplied to the resulting product signals.

More typically, the entire channel content is not cubed; a squared,cubed or other non-linear term adds to the channel content. For exampleif the signal into the channel is y(t), the output could be of the form:

z(t)=a ₁ y(t)+a ₂ y ²(t)+a ₃ y ³(t)+ . . . ,

where a₁, a₂, a₃ etc. are some constants. In a channel with nointermodulation distortion a is zero for all values i>1 and if there isintermodulation distortion a_(i) is non zero for some values of i.Generally the cases of concern have a_(i)≠0 for i=2,3.

As stated above, passive intermodulation distortion on the downlink pathdue, e.g., to cabling and/or connector malfunction can be a seriousproblem for communication system operators. This distortion, bycorrupting existing signals and by occupying bands that are allocatedfor other purposes, can cause the network to fail in achieving itsdesigned throughput capacity.

Embodiments of the present disclosure propose a novel solution to theproblem of identifying intermodulation distortion, including PIM, in asystem by using techniques that classify signals according to theircyclostationary properties. The focus of the following description is onthe LTE (Long Term Evolution) wireless communication standard, however,those of skill in the art will readily understand that the generalprinciples can be equally applied to any other protocol or signal typewith distinguishing cyclostationary features. In addition the describedtechniques and procedures may also be applied to the products of onesignal type with another provided such product signals also exhibitcyclostationary features.

Cyclostationarity of LTE Signals

Cyclostationarity techniques are used in the field of cognitive radio tohypothesize the existence and parameters of various wireless protocols.Since PIM can cause a signal to produce artifacts of itself atfrequencies other than intended, it is sensible to examine whether suchartifacts can be found using cyclostationarity techniques. As we haveobserved in the previous section, if the signals present in somecommunication channel are corrupted due to the presence of a channelnon-linearity, the resultant aggregate signal can have various originalsignal products shifted by various frequencies.

As discussed above, intermodulation distortion results in the product ofinteger powers of distinct signals distributed both in the originalsignal bandwidth and out of this bandwidth. Embodiments of the presentdisclosure consider the intermodulation products caused due tonon-linearities (cabling defects, faulty connections, etc.) throughout asignal reception or transmission system. Other embodiments choosecertain frequency bands to search for “unexpected signals” usingcyclostationarity techniques. To clarify the meaning of an unexpectedsignal as used herein, consider a downlink signal from a communicationnetwork operator. The communication network operator typically has someassigned bandwidth for the aggregate of all the communication signals inthe communication network, an aggregate that could be of the order ofseveral tens of MHz. In this bandwidth, the communication networkoperator likely has multiple cellular protocols in operation. Some ofthis bandwidth is assigned to LTE, other bandwidth is assigned to otherprotocols, perhaps even some residual of protocols such as GSM (GlobalSystem for Mobile Communications) or NRTT (Single Carrier RadioTransmission Technology). There may also be certain unused pieces ofspectrum that the operator has license to but does not use (guard bands,unallocated spectrum, etc.) There also may be certain bands between oradjacent to the assigned bandwidth that are reserved for specialpurposes (national security, etc.) in which communication is restrictedand which bands are often not occupied by signals. Thus, an unexpectedsignal is a signal component that the communication network operator hadno desire to generate but which is nonetheless produced by, for example,defects in the communication network infrastructure.

Suppose several LTE signals are present in the source signals of thiscommunication network operator's downlink. When intermodulationdistortion occurs, the signals mutually amplitude modulate each otherand cause spurious signals to emerge elsewhere as described above. As asimple, non-limiting, example, consider a first LTE signal centered atfrequency f₁ and a second LTE signal centered at frequency f₂. Theintermodulation distortion (assuming third order terms exist) can nowproduce a product signal at a frequency 2f₂−f₁. It can also produce aproduct signal at 2f₂+f₁. Extending this to all possible LTE signals atvarious frequencies we see that a whole range of possible unwantedproduct signals can emerge at a whole range of various frequencies.

As is known in the art, LTE signals are generated as OrthogonalFrequency Division Multiplexed (“OFDM”) signals. To examine the featuresof the product waveforms more carefully, consider two synchronized(i.e., symbol start times coincident) OFDM signals s₁(t) and s₂(t) attwo distinct frequencies f₁ and f₂. Utilizing the complex envelope ofeach waveform, we can then write these signals as:

s ₁(t)=

{{tilde over (s)} ₁(t)e ^((j2πf) ¹ ^(t))}

s ₂(t)=

{{tilde over (s)} ₂(t)e ^((j2πf) ² ^(t))}

Consider a typical term such as p(t)=s₁(t)² s₂(t) that may arise in thepassage of the sum of these OFDM signals through a non-linearity. Forexample, p(t) could occur as a third order intermodulation distortion.Both s₁(t) and s₂(t) exhibit non-conjugate cyclostationarity. To seethis, we can write {tilde over (s)}₁(t) in the OFDM format as

$\begin{matrix}{\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{1}^{N_{c}}\; {d_{ni}^{({j\; 2\; \pi \; \; \Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}}}} & (2.3)\end{matrix}$

where d_(ni) are the complex symbols (QAM or PSK) in each symbol timeT_(s), n is the symbol counter, ε is the unknown symbol timing, N_(c) isthe number of subcarriers, Δf is the subcarrier frequency spacing, andr(t) is a rectangular pulse of width T_(s). The symbol timeT_(s)=T_(u)+T_(g) where T_(u) is the useful symbol time and T_(g) is theguard time. The non-conjugate Cyclic Autocorrelation Function (“CAF”)for the complex signal {tilde over (s)}₁(t) is defined by

$\begin{matrix}{{{R_{s_{1}s_{1}}^{\alpha}(\tau)} = {\lim\limits_{T\rightarrow\infty}{\frac{1}{T}{\int_{- \frac{T}{2}}^{\frac{T}{2}}{E\left\{ {{{\overset{\sim}{s}}_{1}(t)}{{\overset{\sim}{s}}_{1}^{*}\left( {t + \tau} \right)}} \right\} ^{({j\; 2\; \pi \; \alpha \; t})}\ {t}}}}}},} & (2.4)\end{matrix}$

where E{.} is the expectation operator. For a non-cyclostationarysignal, R_(s) ₁ _(s) ₁ ^(α)(t,τ)=0 for all α≠0. Any nonzero value of αfor which the CAF is non-zero is called a cycle frequency of the signals₁(t). The time varying non-conjugate autocorrelation of the OFDM signal

R _(s) _(i) _(s) _(i) (t,τ)=E{{tilde over (s)} ₁(t){tilde over (s)}₁*(t+τ)}

can be written as

$\begin{matrix}{{R_{s_{1}s_{1}}\left( {t,\tau} \right)} = {E\left\{ {\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{i = 1}^{N_{c}}\; {d_{ni}^{({j\; 2\; \pi \; \; \Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}{\sum\limits_{m = {- \infty}}^{\infty}\; {\sum\limits_{k = 1}^{N_{c}}\; {d_{mk}^{*}^{({{- {j2}}\; \pi \; k\; \Delta \; {f{({t + \tau - {mT}_{s} - ɛ})}}})}{r\left( {t + \tau - {mT}_{s} - ɛ} \right)}}}}}}} \right\}}} & (2.5)\end{matrix}$

It may be noted that the only random quantities over which theexpectation operates are the constellation points d_(ni) and d_(mk)*.The only surviving terms in equation (2.5) are those terms where thecomplex modulation symbols are exact conjugates of each other. Theseterms occur only when τ<T_(s) and in such cases the shifted pulsewaveforms intersect in a new pulse waveform of shortened durationresulting in a waveform that is periodic in t. Thus equation (2.5)simplifies to give

$\begin{matrix}{\sum\limits_{m = {- \infty}}^{\infty}\; {A\frac{\sin \left( {\pi \; N_{c}\Delta \; f\; \tau} \right)}{\sin \left( {{\pi\Delta}\; f\; \tau} \right)}{r\left( {t - {nT}_{s} - ɛ} \right)}{r\left( {t + \tau - {nT}_{s} - ɛ} \right)}}} & (2.6)\end{matrix}$

where A is a scalar real multiplier dependent on the specificconstellation d_(i) and mapping of binary data to QAM or PSKconstellation points. This equation is clearly periodic in t with periodT_(s), and hence when the CAF is generated will show spectral lines forcertain values of α. It is instructive to consider what happens whenτ=T_(u). In this case the fractional term in equation (2.6) results inunity. Thus when the data is moved to overlap at exactly the cyclicprefix, the amplitude of the autocorrelation is at a relative maximum.Thus the existence of the cyclic prefix makes the cyclostationaryfeatures of OFDM rise out of the noise floor and make it detectable.

For purposes of this discussion, it is not sufficient that s₁(t) ands₂(t) exhibit cyclostationarity. We want to take a particular thirdorder term such as s₁ ²(t)s₂(t) and show that it too exhibitscyclostationarity. More generally, we want a product such as p(t)=s₁²(t+β)s₂(t) to also exhibit cyclostationarity, at least when β is asmall fraction of T_(s). To show this, we must first attempt to writethe product waveform in terms of its Complex Envelope (“CE”). Now s₁(t)can be written as

s ₁(t)=

{{tilde over (s)} _(i)(t)e ^((j2πf) ¹ ^(t))}=½[{tilde over (s)}₁(t)e^((j2πf) ^(t) ⁾ +{tilde over (s)} ₁*(t)e ^((−j2πf) ¹ ^(t))],  (2.7)

and similarly

s ₂(t)=½[{tilde over (s)}₂(t)e ^((j2πf) ¹ ^(t)) +{tilde over (s)} ₂*(t)e^((j2πf) ¹ ^(t))].  (2.8)

Now we can square the expression for s₁(t) to obtain

s ₁ ²=¼[({tilde over (s)} ₁ ²(t)e ^((j4πf) ¹ ^(t)) +{tilde over (s)}₁*²(t)e ^((−j4πf) ¹ ^(t))+2{tilde over (s)} ₁(t){tilde over (s)}₁*(t)]  (2.9)

When we multiply out the terms in the expansion of s₁ ²(t)s₂(t) we findthat this product can be generated from the complex envelopes given bys₁ ²(t)s₂*(t), {tilde over (s)}₁ ²(t){tilde over (s)}₂(t), and |{tildeover (s)}₁(t)|²{tilde over (s)}₂(t), inclusive of the conjugates of eachterm, and where in the first case the applicable carrier frequency is2f₁−f₂, in the second case the carrier frequency is 2f₁+f₂ and in thethird case it is f₂.

Thus, the question now becomes whether any of the above three componentsof the product waveform is capable of exhibiting cyclostationarity. Itturns out that all three exhibit cyclostationarity. Let us show thisfirst in the simplified case where β=0 (synchronized signals).

We now present a novel and useful result which greatly simplifies thetask of exhibiting cyclostationarity for these waveforms: the product ofthe CE's of any number of synchronized OFDM signals is the CE of adifferent OFDM signal. To show this, consider the product of two OFDMCEs,

$\begin{matrix}{{\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{i = 1}^{N_{c}}\; {d_{ni}^{({{j2\pi}\; {\Delta}\; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}{\sum\limits_{m = {- \infty}}^{\infty}\; {\sum\limits_{k = 1}^{N_{c}}\; {d_{mk}^{({{j2\pi}\; k\; \Delta \; {f{({t - {mT}_{s} - ɛ})}}})}{r\left( {t - {mT}_{s} - ɛ} \right)}}}}}}},} & (2.10)\end{matrix}$

which, noting that the only terms remaining when the two sums aremultiplied are the terms with the same index on the pulse waveforms,results in

$\begin{matrix}{{{\sum\limits_{n = {- \infty}}^{\infty}\; \left\{ {\sum\limits_{i = 1}^{N_{c}}\; {d_{ni}^{({j\; 2\; \pi \; {\Delta}\; {f{({t - {nT}_{s} - ɛ})}}})}{\sum\limits_{k = 1}^{N_{c}}\; {d_{nk}^{({{j2\pi}\; k\; \Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}}}}} \right\}} = {{\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{i = 1}^{N_{c}}\; {\sum\limits_{k = 1}^{N_{c}}\; {d_{nk}d_{ni}^{({{j2\pi \Delta}\; {f{({t - {nT}_{s} - ɛ})}}})}^{({j\; 2\; \pi \; k\; \Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}}}}} = {{\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{i = 1}^{N_{c}}\; {\sum\limits_{k = 1}^{N_{c}}\; {d_{nk}d_{ni}^{({j\; 2\; {\pi {({i + k})}}\Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}}}}} = {\sum\limits_{n = {- \infty}}^{\infty}\; {\sum\limits_{m = 1}^{2\; N_{c}}\; {D_{nm}^{({j\; 2\; \pi \; m\; \Delta \; {f{({t - {nT}_{s} - ɛ})}}})}{r\left( {t - {nT}_{s} - ɛ} \right)}}}}}}},} & (2.11)\end{matrix}$

in which m=(i+k) and {D_((.))} is a new constellation. Equation (2.11)can now be recognized as identical to the CE of a different OFDM signal(e.g., equation (2.3)) whose constellation is formed by the product ofthe individual constellations of the two signals and where the span ofthe sub-carriers is the sum of the previous spans (with the samesub-carrier spacing). The extension to the product of more than two OFDMCEs follows by induction; for three terms, take the first two, apply theresult and then apply it to the product of the first two and the thirdterm.

This result makes it immediately obvious that all the terms referred toearlier in the product waveform will exhibit cyclostationarity withexactly the same cycle frequencies as the base signals. Thus for OFDMsignals, all the PIM products (of any order) of synchronous signals willexhibit cyclostationarity. We also note that self-products, namely termswhich involve integer powers of one particular signal, behave similarly.

Now consider the question of whether a product such as p(t)=s₁(t+β)s₂(t)also exhibits cyclostationarity when β≠0. This is harder to demonstratemathematically in an exact manner, so we will approach this differently.

Consider signals s₁(t), s₂(t) where the signal in any symbol time is nota sum of subcarriers but rather a single subcarrier. It is clear thatthe actual OFDM signals are then obtained by aggregating N_(c) suchsignals in each symbol time, but it is easier to make the case by firstfocusing on the single carrier signals. As previously, we assume thatthe cyclic prefix fraction or guard time is the same for both signals.Now, placing our attention on a single symbol time, if the signals weresynchronized, then the product signal content is the same in the first[0,T_(g)] segment of p(t) and the final [T_(s)−T_(g),T_(s)] segment.That is, there is a repetition of the signal content that occurs with adelay T_(u). This is another way to argue for the cyclostationaryproperties in the synchronized case.

Now let us assume that β is a small fraction of T_(g). Then, the effectof β is to slightly stagger a symbol time of s₁(t) with respect to asymbol time of s₂(t). What we then see is that there is still arepetition of terms in the product in the segments [0, T_(g)−β] and[T_(s)−T_(g)+β,T_(s)]. Thus, the autocorrelation of the product signalat delay T_(u) will produce energy equal to that with zero delay. Thismeans that there is still a repeated component in the product waveform,and hence implies the likely existence of a cyclostationary feature thatmay be detectable. As β increases, this feature will diminish in sizeand when β≧T_(g) the feature should disappear. The most importantobservation here is that a cyclostationary feature may be observable ifthe de-synchronization (expressed using β) is small relative to theguard time.

Identifying Passive Intermodulation Distortion on LTE Signals

All of the possible frequencies or frequency bands where intermodulationproducts could possibly exist are computable given knowledge of thechannel or frequency map used by the communication network operator. Letthis set of possible frequencies (or frequency bands) at whichundesirable LTE product signals occur be denoted by F. Then one canpropose examining each candidate frequency or frequency band in F forthe following hypotheses:

H1: Does it exhibit the presence of an LTE product signal? More strictlydoes a cyclostationarity analysis of this candidate frequency orfrequency band exhibit a positive test for LTE?

H2: In an ideal situation, should this frequency or frequency bandexhibit LTE cyclostationary features?

If H1 is answered in the affirmative and H2 in the negative, it is thenpossible for us to argue that the communication network operator clearlyhas a defect in his network. One possible and likely explanation forthis defect is that he or she has unrecognized intermodulationdistortion actively degrading the system.

One novel aspect in the exemplary embodiments is that we search forproducts of LTE signals (i.e., one LTE signal raised to some integerpower times one or more other LTE signals raised to some integer powers)in the Radio Frequency domain, optionally convert these product signalsto baseband and then apply cyclostationarity detection techniques toanswer the hypotheses tests H1 and H2. Note that the signals are notalways assumed to be perfectly synchronized; that is, one signal couldhave some offset in time with respect to where the other signal orsignals starts.

In an embodiment, if we were searching for an intermodulation product atfrequency 2f₂+f₁, where f₂ and f₁ are the RF frequencies of the LTEsignals, we might downconvert the signals by suitable quadraturedownconversion using a frequency of 2f₂+f₁ and then examine thisbaseband signal for LTE features. In another embodiment, theintermodulation product at frequency 2f₂+f₁ need not be downconverted.We note that there is a plethora of possible linear frequencycombinations that can be searched based mainly on a positive response tothe query in H2. Our finding is that the LTE product signals exhibit aunique Cyclic Autocorrelation Function (“CAF”) provided the cyclicprefix on the signals is not zero, and provided that the signals aresynchronized to within approximately 75% of the cyclic prefix length.For example, if the cyclic prefix is of size 25% of the symbol time, wethen need to be synchronized to within about 18% of the symbol time.Since we can identify LTE product signals in this manner, we then have ascheme that produces a positive result in the presence ofintermodulation distortion. With respect to LTE, other embodiments canexploit the cyclostationary features of the LTE reference signal, wherewhen we consider signal products we can additionally search for morefeatures if one of the LTE signals was a reference signal.

In some variations of the LTE communication signals it may be necessaryto provide further filtering of the signals in the time or frequencydomain prior to applying cyclostationarity analysis. One such example isthe case where LTE does not operate in the extended mode. In such casesthe relative size of the Cyclic Prefix (“CP” or guard time) may changein some deterministic manner. In all such cases, by suitable excision ofsignal segments in the time domain the excised signals will preservecyclostationary features. Such excision operations in time or filteringoperations in frequency are contemplated herein and can precede any ofthe techniques presented in this disclosure.

In the time domain, different time intervals within LTE are expressed asmultiples of a basic time unit T_(s)= 1/30720000 seconds. The radioframe has a length of 10 ms; (T₁=307200T_(s)). Each frame is dividedinto ten equally sized sub-frames of 1 ms in length. Scheduling is doneon a sub-frame basis for both the downlink and uplink. Each sub-framemay consists of two equally sized slots of 0.5 ms in length. Each slotin turn consists of a number of OFDM symbols which can be either seven(normal cyclic prefix) or six (extended cyclic prefix). The usefulsymbol time is Tu=2048×T_(s)≈66.7 μs. For the normal mode, the firstsymbol has a cyclic prefix of length TCP=160×T_(s)≈5.2 ρs. The remainingsix symbols have a cyclic prefix of length TCP=144×T_(s)≈4.7 μs. Thereason for a different CP length of the first symbol is to make theoverall slot length in terms of time units divisible by 15360. For theextended mode, the cyclic prefix is TCP_(e)=512×T_(s)≈16.7 μs. Bydesign, the CP is longer than the typical delay spread of a fewmicroseconds typically encountered in practice. The normal cyclic prefixis used in urban cells and high data rate applications while theextended cyclic prefix is used in special cases like multi-cellbroadcast and in very large cells (e.g. rural areas, low data rateapplications). When the normal cyclic prefix is used, data extracted forcyclostationary analysis can be excised by removing the first symbol ofevery slot. In the extended mode, no such modification of the data isneeded. In general, therefore, it is quite feasible, and contemplatedherein, to accommodate small variations in signaling formats that mayocclude cyclostationary features by intelligently modifying theextracted data prior to analysis.

With attention drawn to FIG. 1, a flow chart 100 for identifying asignal according to an embodiment of the present subject matter ispresented. At block 101, the presence of a first signal in a frequencyband is determined where the first signal is the product of a second andthird signal. At block 102, a cyclostationarity detection technique isapplied to the first signal. At block 103, the first signal isidentified from the results of the application of the cyclostationaritydetection technique to the first signal. In an embodiment, thecyclostationarity detection technique includes determining a cyclicautocorrelation function of the first signal. In another embodiment, theresults of applying the cyclostationarity detection technique to thefirst signal include determining if the first signal includes apredetermined characteristic of either the second or third signal. Thepredetermined characteristic may be one or more of a cyclicprefix-induced cyclostationarity, a frame rate, and a chip rate.

In yet another embodiment, one or both of the second and third signalsis a communication signal (e.g., a signal that is intended by theoperator of a communication system to carry useful information), acommunication signal in a wireless communication system, an OrthogonalFrequency Division Multiplexed (“OFDM”) signal, or a Long Term Evolution(“LTE”) signal. In still a further embodiment, one or both of the secondand third signals is a communication signal in a wireless communicationsystem but the first signal is not a communication signal in thewireless communication system. In yet still a further embodiment, one orboth of the second and third signals is a tone, a modulated carrier, ornoise.

Now turning to FIG. 2, a functional block diagram 400 for identifying asignal according to an embodiment of the present subject matter isdepicted. In an embodiment, mobile device 210 communicates, via radiofrequency (“RF”) uplink and downlink channels, as is known in the art,with wireless transmitter 220 in a wireless communication network. Theuplink and/or downlink channel may be composed of one or more frequencybands. It will be understood by those of skill in the art that thepresent exemplary embodiment is non-limiting and that other embodimentsof the present disclosure, including use in a wired system, arecontemplated herein. The wireless communication network also includes aprocessor 230 which is operatively connected to transmitter 220 and amemory device 240. The processor 230 includes a signal presence circuit231, a detection circuit 232, and an identification circuit 233.

In an embodiment, the signal presence circuit 231 determines thepresence of a first signal in a frequency band, such as, but not limitedto, a frequency band in a downlink channel, where the first signal isthe product of a second and third signal. The detection circuit 232applies a cyclostationarity detection technique to the first signal. Theidentification circuit 233 identifies the first signal from the resultsof the application of the cyclostationarity detection technique to thefirst signal in the detection circuit 232. In an embodiment, thedetection circuit 232 includes circuitry which determines a cyclicautocorrelation function of the first signal. In another embodiment, theidentification circuit 232 includes circuitry which determines if thefirst signal includes a predetermined characteristic of either thesecond or third signal. The predetermined characteristic may be one ormore of a cyclic prefix-induced cyclostationarity, a frame rate, and achip rate. The predetermined characteristic may be stored in the memorydevice 240.

In yet another embodiment, one or both of the second and third signalsis a communication signal (e.g., a signal that is intended by theoperator of a communication system to carry useful information) ineither an uplink or downlink channel, a communication signal in awireless communication system, an Orthogonal Frequency DivisionMultiplexed (“OFDM”) signal, or a Long Term Evolution (“LTE”) signal. Instill a further embodiment, one or both of the second and third signalsis a communication signal, in either an uplink or downlink channel, in awireless communication system but the first signal is not acommunication signal in the wireless communication system. In yet stilla further embodiment, one or both of the second and third signals is atone, a modulated carrier, or noise.

In another embodiment, the processor 230 is programmed using anon-transitory machine-readable medium which stores executableinstructions to be executed by the processor 230 to implement a methodof identifying a signal. In an embodiment, the method includes the stepsof determining the presence of a first signal in a frequency band wherethe first signal is the product of a second and third signal, applying acyclostationarity detection technique to the first signal, andidentifying the first signal from the results of the application of thecyclostationarity detection technique to the first signal. In anembodiment, the cyclostationarity detection technique includesdetermining a cyclic autocorrelation function of the first signal. Inanother embodiment, the results of applying the cyclostationaritydetection technique to the first signal include determining if the firstsignal includes a predetermined characteristic of either the second orthird signal. The predetermined characteristic may be one or more of acyclic prefix-induced cyclostationarity, a frame rate, and a chip rate.

In yet another embodiment, one or both of the second and third signalsis a communication signal (e.g., a signal that is intended by theoperator of a communication system to carry useful information), acommunication signal in a wireless communication system, an OrthogonalFrequency Division Multiplexed (“OFDM”) signal, or a Long Term Evolution(“LTE”) signal. In still a further embodiment, one or both of the secondand third signals is a communication signal in a wireless communicationsystem but the first signal is not a communication signal in thewireless communication system. In yet still a further embodiment, one orboth of the second and third signals is a tone, a modulated carrier, ornoise.

FIG. 3 illustrates a flow chart 300 for determining intermodulationdistortion of a radio frequency product signal according to anembodiment of the present subject matter. At block 301, a frequency or afrequency band, in either an uplink or downlink channel, is searched foran RF product signal. The RF product signal is a product of a first RFsignal raised to the power of a first integer and a second RF signalraised to the power of a second integer. Additionally, the first RFsignal is at a first frequency or frequency band, the second RF signalis at a second frequency or frequency band, and the RF product signal isat a third frequency or frequency band. At block 302, acyclostationarity detection technique is applied to the RF productsignal. At block 303, the RF product signal is identified as anintermodulation distortion signal from the results of the application ofthe cyclostationarity detection technique to the RF product signal. Inan embodiment, the first and second RF signals are transmitted by acommunication system. In a further embodiment, at block 304 adetermination is made as to whether the frequency or frequency band ofthe RF product signal is a frequency or frequency band transmitted bythe communication system, i.e., whether the detected cyclostationarycharacteristic is expected in the frequency band.

In an embodiment, the first RF signal is transmitted by a firstcommunication system and the second RF signal is transmitted by a secondcommunication system. In a further embodiment, a determination is madeas to whether the third frequency or frequency band is a frequency orfrequency band transmitted by either the first or second communicationsystem, i.e., whether the detected cyclostationary characteristic isexpected in the frequency band. The first and second communicationsystems may operate using different communication protocols.

As discussed above, the RF product signal is a product of a first RFsignal raised to the power of a first integer and a second RF signalraised to the power of a second integer. In an embodiment, the first andsecond integers are the same. In another embodiment, the sum of thefirst and second integers equals three.

In yet a further embodiment, the RF product signal includes a cyclicprefix, as is known in the art. In still a further embodiment, the firstand second RF signals each include a cyclic prefix having apredetermined length and the first and second RF signals aresynchronized to within at least 75% of the predetermined length of thecyclic prefix.

In an embodiment, the cyclostationarity detection technique includesdetermining a cyclic autocorrelation function of the first signal. Inanother embodiment, the results of applying the cyclostationaritydetection technique to the RF product signal include determining if theRF product signal includes a predetermined characteristic of either thefirst or second RF signal. The predetermined characteristic may be oneor more of a cyclic prefix-induced cyclostationarity, a frame rate, anda chip rate.

In yet another embodiment, one or both of the first and second RFsignals is a communication signal (e.g., a signal that is intended bythe operator of a communication system to carry useful information), acommunication signal in a wireless communication system, an OrthogonalFrequency Division Multiplexed (“OFDM”) signal, or a Long Term Evolution(“LTE”) signal. In still a further embodiment, one or both of the firstand second RF signals is a communication signal in a wirelesscommunication system but the RF product signal is not a communicationsignal in the wireless communication system. In yet still a furtherembodiment, one or both of the first and second RF signals is a tone, amodulated carrier, or noise.

Considering FIG. 4, a functional block diagram 400 for determiningintermodulation distortion of a radio frequency product signal accordingto an embodiment of the present subject matter is depicted. In anembodiment, mobile device 410 communicates, via radio frequency (“RF”)uplink and downlink channels, as is known in the art, with wirelesstransmitter 420 in a wireless communication network. The uplink and/ordownlink channel may be composed of one or more frequency bands. It willbe understood by those of skill in the art that the present exemplaryembodiment is non-limiting and that other embodiments of the presentdisclosure, including use in a wired system, are contemplated herein.The wireless communication network also includes a processor 430 whichis operatively connected to transmitter 420 and a memory device 440. Theprocessor 430 includes an RF product signal search circuit 431, adetection circuit 432, and an identification circuit 433. In furtherembodiments, the processor 430 further includes one or both of circuit434 and circuit 435, as discussed in further detail below.

In an embodiment, the RF product signal search circuit 431 searches afrequency or a frequency band, in either an uplink or downlink channel,for an RF product signal. The RF product signal is a product of a firstRF signal raised to the power of a first integer and a second RF signalraised to the power of a second integer. Additionally, the first RFsignal is at a first frequency or frequency band, the second RF signalis at a second frequency or frequency band, and the RF product signal isat a third frequency or frequency band. The detection circuit 432applies a cyclostationarity detection technique to the RF productsignal. The identification circuit 433 identifies the RF product signalas an intermodulation distortion signal from the results of theapplication of the cyclostationarity detection technique to the RFproduct signal. In an embodiment, the first and second RF signals aretransmitted by a communication system. In a further embodiment, circuit434 determines whether the frequency or frequency band of the RF productsignal is a frequency or frequency band transmitted by the communicationsystem, i.e., whether the detected cyclostationary characteristic isexpected in the frequency band.

In another embodiment, the first RF signal is transmitted by a firstcommunication system and the second RF signal is transmitted by a secondcommunication system. In a further embodiment, circuit 435 determineswhether the third frequency or frequency band is a frequency orfrequency band transmitted by either the first or second communicationsystem, i.e., whether the detected cyclostationary characteristic isexpected in the frequency band. The first and second communicationsystems may operate using different communication protocols.

As discussed above, the RF product signal is a product of a first RFsignal raised to the power of a first integer and a second RF signalraised to the power of a second integer. In an embodiment, the first andsecond integers are the same. In another embodiment, the sum of thefirst and second integers equals three.

In yet a further embodiment, the RF product signal includes a cyclicprefix, as is known in the art. In still a further embodiment, the firstand second RF signals each include a cyclic prefix having apredetermined length and the first and second RF signals aresynchronized to within at least 75% of the predetermined length of thecyclic prefix.

In an embodiment, the cyclostationarity detection technique applied bythe detection circuit 432 includes circuitry which determines a cyclicautocorrelation function of the RF product signal. In anotherembodiment, the identification circuit 433 includes circuitry whichdetermines if the RF product signal includes a predeterminedcharacteristic of either the first or second RF signal. Thepredetermined characteristic may be one or more of a cyclicprefix-induced cyclostationarity, a frame rate, and a chip rate.

In yet another embodiment, one or both of the first and second RFsignals is a communication signal (e.g., a signal that is intended bythe operator of a communication system to carry useful information), acommunication signal in a wireless communication system, an OrthogonalFrequency Division Multiplexed (“OFDM”) signal, or a Long Term Evolution(“LTE”) signal. In still a further embodiment, one or both of the firstand second RF signals is a communication signal in a wirelesscommunication system but the RF product signal is not a communicationsignal in the wireless communication system. In yet still a furtherembodiment, one or both of the first and second RF signals is a tone, amodulated carrier, or noise.

In another embodiment, the processor 430 is programmed using anon-transitory machine-readable medium which stores executableinstructions to be executed by the processor 430 to implement a methodof determining intermodulation distortion. In an embodiment, the methodincludes the step of searching a frequency or a frequency band, ineither an uplink or downlink channel, for an RF product signal. The RFproduct signal is a product of a first RF signal raised to the power ofa first integer and a second RF signal raised to the power of a secondinteger. Additionally, the first RF signal is at a first frequency orfrequency band, the second RF signal is at a second frequency orfrequency band, and the RF product signal is at a third frequency orfrequency band. The method also includes the steps of applying acyclostationarity detection technique to the RF product signal, andidentifying the RF product signal as an intermodulation distortionsignal from the results of the application of the cyclostationaritydetection technique to the RF product signal. In an embodiment, thefirst and second RF signals are transmitted by a communication system.In a further embodiment, the method further includes the step ofdetermining whether the frequency or frequency band of the RF productsignal is a frequency or frequency band transmitted by the communicationsystem, i.e., whether the detected cyclostationary characteristic isexpected in the frequency band.

In an embodiment, the first RF signal is transmitted by a firstcommunication system and the second RF signal is transmitted by a secondcommunication system. In a still further embodiment, the method includesthe step of determining whether the third frequency or frequency band isa frequency or frequency band transmitted by either the first or secondcommunication system, i.e., whether the detected cyclostationarycharacteristic is expected in the frequency band. The first and secondcommunication systems may operate using different communicationprotocols.

As discussed above, the RF product signal is a product of a first RFsignal raised to the power of a first integer and a second RF signalraised to the power of a second integer. In an embodiment, the first andsecond integers are the same. In another embodiment, the sum of thefirst and second integers equals three.

In yet a further embodiment, the RF product signal includes a cyclicprefix, as is known in the art. In still a further embodiment, the firstand second RF signals each include a cyclic prefix having apredetermined length and the first and second RF signals aresynchronized to within at least 75% of the predetermined length of thecyclic prefix.

In an embodiment, the cyclostationarity detection technique includesdetermining a cyclic autocorrelation function of the first signal. Inanother embodiment, the results of applying the cyclostationaritydetection technique to the RF product signal include determining if theRF product signal includes a predetermined characteristic of either thefirst or second RF signal. The predetermined characteristic may be oneor more of a cyclic prefix-induced cyclostationarity, a frame rate, anda chip rate.

In yet another embodiment, one or both of the first and second RFsignals is a communication signal (e.g., a signal that is intended bythe operator of a communication system to carry useful information), acommunication signal in a wireless communication system, an OrthogonalFrequency Division Multiplexed (“OFDM”) signal, or a Long Term Evolution(“LTE”) signal. In still a further embodiment, one or both of the firstand second RF signals is a communication signal in a wirelesscommunication system but the RF product signal is not a communicationsignal in the wireless communication system. In yet still a furtherembodiment, one or both of the first and second RF signals is a tone, amodulated carrier, or noise.

Identifying Passive Intermodulation Distortion on UMTS Signals

The method to be applied for UMTS signals is identical to that for LTEsignals. UMTS signals have specific cyclostationary signatures just asLTE signals have signatures such as those we have discussed. Cyclicfrequencies at multiples of both the inverse chip time and the inverseframe time may be recognized in the various order product signals thatoccur as a result of PIM. Once again, these product signals will occurwith frequency translations corresponding to the PIM order.

Candidate Algorithms for Identifying PIM

We now consider two possible algorithms for identifying PIM in theaggregate communication channels of a communication system. Typically,in an embodiment, these may be the entire downlink (“DL”) of a wirelesssystem in a given cell or sector. In both of these algorithms we operateunder the assumption of operating in co-operation with the network(communication system) operator. Clearly, various other algorithms basedon the techniques and procedures disclosed herein are possible.

In an embodiment, the network frequency plan for, e.g., a communicationnetwork is obtained. An assumption may be made regarding the presence ofsome form of PIM generating intermodulation of a specific form.Typically, the likelihood of PIM is initially set to zero. Then for eachexisting LTE channel pair compute where product signals could exist.These define a set of candidate frequency bins. In an embodiment, forthe content in each such bin construct the complex envelope. In anotherembodiment, the candidate frequency bin content is first downconvertedto baseband. With the complex envelope available, subject the complexenvelope to cyclostationarity analysis. In an embodiment, one would tuneto a particular bandwidth and run the CAF generating routines for aconfigurable time. Running such a routine for several minutes may beneeded to draw cyclostationary features out of the noise. The hypothesestests H1 and H2 as indicated above can now be performed. If one winds upwith a positive result for H1 and a negative result for H2, then thelikelihood of PIM in the candidate frequency bin is increased. In anembodiment, this procedure may be repeated over all candidate frequencybins. Finally, if the likelihood of PIM is greater than someconfigurable threshold, a decision that PIM exists in this aggregate ofchannels is made.

In an embodiment, the network frequency plan for, e.g., a communicationnetwork is obtained. Typically, the likelihood of PIM is initially setto zero. Partition the entire bandwidth to be tested into a set offrequency bins. In an embodiment, one may start with the smallestassignable LTE channel bandwidth and work up to the largest possible. Inan embodiment, for the content in each such bin construct the complexenvelope. In another embodiment, the candidate frequency bin content isfirst downconverted to baseband. With the complex envelope available,subject the complex envelope to cyclostationarity analysis. In anembodiment, one would tune to a particular bandwidth and run the CAFgenerating routines for a configurable time. Running such a routine forseveral minutes may be needed to draw cyclostationary features out ofthe noise. The hypotheses tests H1 and H2 as indicated above can now beperformed. If one winds up with a positive result for H1 and a negativeresult for H2, then, in an embodiment, a computation is initiated. Thiscomputation calculates which possible LTE channel pair in the frequencyplan could possibly generate a PIM product in the bin under test. Thecalculation is repeated for various possible intermodulation orders. Ifsuch a pair of valid LTE channels and a valid intermodulation orderexists, the likelihood of PIM is increased. In an embodiment, the aboveprocedure is repeated over all candidate frequency bins. Finally, if thelikelihood of PIM is greater than some configurable threshold, adecision that PIM exists in this aggregate of channels is made.

Considering now FIG. 5, a flow chart for determining radio frequencysignals causing intermodulation distortion according to an embodiment ofthe present subject matter is presented. At block 501, a frequency binis selected. The frequency bin may be selected based on a pair ofsignals from the predetermined set of RF signals. At block 502, acomplex envelope is generated for a first signal in the frequency bin.At block 503, a cyclic autocorrelation function (“CAF”) for the firstsignal is determined. At block 504, the determined cyclicautocorrelation function is compared to a cyclic autocorrelationfunction for the predetermined signal type. At block 505, the frequencyof the first signal is compared with the frequency of the predeterminedset of RF channels.

In a further embodiment, at block 506, a plurality of the RF channelsthat produced the first signal is determined. In a still furtherembodiment, at block 507, an intermodulation order for each of theplurality of RF channels that produced the first signal is determined.

In another embodiment, the step of comparing the determined cyclicautocorrelation function to a cyclic autocorrelation function for thepredetermined signal type includes determining if the first signalcomprises a predetermined characteristic of the predetermined signaltype. The predetermined characteristic may be one or more of a cyclicprefix-induced cyclostationarity, a frame rate, and a chip rate.

In yet another embodiment, one or both of the plural RF channels is acommunication signal (i.e., a signal that is intended by the operator ofa communication system to carry useful information) in either an uplinkor downlink channel, an Orthogonal Frequency Division Multiplexed(“OFDM”) signal, or a Long Term Evolution (“LTE”) signal. In yet stillanother embodiment, the first signal is not a communication signal inthe communication system. In a further embodiment, one or both of theplurality of RF channels is a tone, a modulated carrier, or noise.

FIG. 6 depicts a functional block diagram for determining radiofrequency signals causing intermodulation distortion according to anembodiment of the present subject matter. In an embodiment, mobiledevice 610 communicates, via radio frequency (“RF”) uplink and downlinkchannels, as is known in the art, with wireless transmitter 620 in awireless communication network. The uplink and/or downlink channel maybe composed of one or more frequency bands. It will be understood bythose of skill in the art that the present exemplary embodiment isnon-limiting and that other embodiments of the present disclosure,including use in a wired system, are contemplated herein. The wirelesscommunication network also includes a processor 630 which is operativelyconnected to transmitter 620 and a memory device 640. The processor 630includes frequency bin selection circuit 631, a complex envelopegeneration circuit 632, a cyclic autocorrelation function (“CAF”)determining circuit 633, a CAF comparison circuit 634, and a frequencycomparison circuit 635.

In another embodiment, circuit 631 includes circuitry for selecting thefrequency bin based on a pair of signals from the predetermined set ofRF signals.

In a further embodiment, processor 630 also includes circuit 636 whichdetermines a plurality of the RF channels that produced the firstsignal. In a still further embodiment, processor 630 also includescircuit 637 which determines an intermodulation order for each of theplurality of RF channels that produced the first signal is determined.

In another embodiment, circuit 634 includes circuitry for determining ifthe first signal comprises a predetermined characteristic of thepredetermined signal type. The predetermined characteristic may be oneor more of a cyclic prefix-induced cyclostationarity, a frame rate, anda chip rate.

In yet another embodiment, one or both of the plural RF channels is acommunication signal (i.e., a signal that is intended by the operator ofa communication system to carry useful information) in either an uplinkor downlink channel, an Orthogonal Frequency Division Multiplexed(“OFDM”) signal, or a Long Term Evolution (“LTE”) signal. In yet stillanother embodiment, the first signal is not a communication signal inthe communication system. In a further embodiment, one or both of theplurality of RF channels is a tone, a modulated carrier, or noise.

In another embodiment, the processor 630 is programmed using anon-transitory machine-readable medium which stores executableinstructions to be executed by the processor 630 to implement a methodfor determining radio frequency signals causing intermodulationdistortion. In an embodiment, the method includes the steps of selectinga frequency bin, where the frequency bin may be selected based on a pairof signals from the predetermined set of RF signals, generating acomplex envelope for a first signal in the frequency bin, determining acyclic autocorrelation function for the first signal, comparing thedetermined cyclic autocorrelation function to a cyclic autocorrelationfunction for the predetermined signal type, and comparing the frequencyof the first signal with the frequency of the predetermined set of RFchannels.

In a further embodiment, the method includes the step of determining aplurality of the RF channels that produced the first signal. In a stillfurther embodiment, the method includes the step of determining anintermodulation order for each of the plurality of RF channels thatproduced the first signal.

In another embodiment, the step of comparing the determined cyclicautocorrelation function to a cyclic autocorrelation function for thepredetermined signal type includes determining if the first signalcomprises a predetermined characteristic of the predetermined signaltype. The predetermined characteristic may be one or more of a cyclicprefix-induced cyclostationarity, a frame rate, and a chip rate.

In yet another embodiment, one or both of the plural RF channels is acommunication signal (i.e., a signal that is intended by the operator ofa communication system to carry useful information) in either an uplinkor downlink channel, an Orthogonal Frequency Division Multiplexed(“OFDM”) signal, or a Long Term Evolution (“LTE”) signal. In yet stillanother embodiment, the first signal is not a communication signal inthe communication system. In a further embodiment, one or both of theplurality of RF channels is a tone, a modulated carrier, or noise.

Optional Pre-Filtering

In an embodiment, we may also note that in those cases where a region ofspectrum to be examined contains a particular signal that is not ofinterest to us, it may be possible to use well known signal extractiontechniques to first extract that particular signal and then subject theresidual to cyclostationarity tests for the product signals of interest.Such methods may be viewed as nulling nuisance or interferer signals inthe spectrum prior to searching for PIM. Note that such nulling mayitself use a cyclostationary technique to remove an interferer if thecycle frequencies for this interferer are distinct from those of theproduct waveforms.

Operation with Multiple Signal Types

In another embodiment, consider a case where a PIM product of one signaltype may occur in spectrum allocated to or containing a different signaltype. An example of such a situation may be where an OFDM PIM productmay occur in spectrum containing a UMTS signal. In such cases, one canapply cyclostationary techniques that ignore the second signal type. TheCAF can be examined directly for cyclic frequencies corresponding to theOFDM signals. This is possible since the cyclic frequencies of thesignal types are distinct. Generally, therefore, if two or more signaltypes coexist, provided they have different cyclostationarycharacteristics, one can compute the CAF for the aggregate signal (thetotal signal in the spectrum) and focus attention on the features oneexpects for the product signals of interest.

Distinguishing Product Signals from Non-Product Signals

In an embodiment, consider a situation where a tentative identificationof a particular product signal type has been made using cyclostationarymethods. Now it may happen that there is some non-zero probability thatthe examined spectrum may have contained a non-product signal of thesame type from some far transmitter. In such cases, further processingmay be needed to affirm or negate the decision on the signal type. Onemethod of excluding a non-product signal would be to attempt todemodulate the signal in the spectrum using a standard demodulator forthat signal type. Provided the SNR is high enough that such ademodulation can be performed, a product signal may not generate a validdemodulated signal. Thus a clean demodulation of the spectrum contentmay indicate that this cannot be a product signal. Note that in the caseof OFDM, as we have shown in previous sections, the product signal couldexhibit an expanded constellation. So in such cases, the demodulationwill show a signal behavior that would not have been expected as astandard OFDM signal. Secondary techniques such as this or othermodulation tests may need to be applied to further confirm or negate adecision on whether the source of a signal in some spectrum is PIM orsome non-product signal (a regular transmission).

Exploiting PIM Induced Subcarrier Interaction in OFDM Signals

In an embodiment, when one examines the effect of PIM on a single LTEsignal, an interesting feature of the LTE signal can be observed. An LTEsignal, as discussed previously, is generated using OFDM. At a veryrudimentary level OFDM is simply an aggregation of tones (subcarriers)with each tone having a particular amplitude and phase. Thus, one canresort to the very elementary exposition of PIM via tone interaction toargue that the effect of PIM on an OFDM signal is that new tones aregenerated with different amplitudes and phases.

Consider two subcarriers of an OFDM signal within an OFDM symbolduration. Let these two subcarriers be the tones with frequencies f₁ andf₂. If the subcarrier spacing is Δf, then with some integer value k,f₂=f₁+kΔf. Now assume there is third order PIM present in the channelcarrying the signal. This can cause a product signal with frequencyf_(PIM)=2f₁−f₂. Substituting for f₂ this gives f_(PIM)=f₁−kΔf. Thistells us that a PIM product occurs at a frequency kΔf below f₁. If Δf=15kHz, then a PIM product occurs an integer multiple of 15 kHz below f₁.

Now considering all the subcarriers in the OFDM signal we see that these“self-product” terms generate signals at frequency shifts with aninteger multiple of the subcarrier spacing from the original set ofsubcarriers. Some of the self-products may occur at frequencies that arecompletely distinct from the set of OFDM subcarriers. If theseself-products can be recognized by some means then that would increasethe likelihood that PIM is present in the signal channel.

Primary Synchronization Channel

As a particular example of how to exploit the PIM induced self-productof OFDM signals, in an embodiment, one can consider the PrimarySynchronization Sequence (“PSS”) in the Primary Synchronization Channel(“P-SCH”) of LTE. In a Frequency Division Duplex (“FDD”) LTE system, thePSS is mapped to the last symbol of slot number 0 and slot number 10 ina particular radio frame. In a Time Division Duplex (“TDD”) system, thePSS is mapped to the third OFDM symbol in sub-frames 1 and 6. In eithercase, the manner in which this is done is to apply a specific complexdomain Zadoff-Chu sequence to 62 middle subcarriers of a 72 subcarrierwindow. Thus there are 10 reserved subcarriers that do not have anyapplied data. It follows that tones induced by PIM will result infrequency components in these reserved subcarriers.

Since the PSS repeats cyclically every half-frame with exactly the samedata (the Zadoff-Chu sequence) then one can propose the recognition ofthe PIM induced energy. To implement this we can exploit the highlyefficient and elegant aspect of OFDM demodulation offered by the FastFourier Transform (“FFT”). Consider the 72-point FFT that may be appliedto data demodulate the content of the PSS carrying symbol. Clearly ifthere were no PIM, there should be no data (energy) in the reservedsubcarriers after an FFT demodulation. With PIM on the other hand, therewill be data in these subcarriers, hence the FFT will result in somefrequency domain content in the reserve subcarriers. Since the PSS isperiodic, the frequency domain content will also be periodic. Thus, onecould consider the autocorrelation of the P-SCH in the frequency domainwhich will then exhibit a cyclostationary feature. One could alsointerpret this as a delay-multiply-integrate loop where the delay is ahalf-frame and where the multiply is the multiplication of the frequencybins corresponding to the reserve subcarriers, and where the integrationis simply a continuing addition of output of the multiplier. Theprocessing gain offered by the integration is limited only by the driftof the PIM behavior over time. If the PIM is static, the method shouldvirtually guarantee detection.

It should be noted that even if there were no reserved subcarriers(essentially a set of frequency bins where no signal exists), anyperiodically recurring PIM product of a fixed set of subcarriers couldbe recognized by the above means. The requirement for this to bepossible is that the PIM product should not share spectrum with someother signal which is also periodic with the same period. Thus, if thePIM generated signal were to fall where some other random non-periodicsignal did, the PIM product should still be detectable (albeit withgreater processing effort).

Certain embodiments of the present disclosure may be implemented by ageneral purpose computer programmed in accordance with the principalsdiscussed herein. It may be emphasized that the above-describedembodiments are merely possible examples of implementations, merely setforth for a clear understanding of the principles of the disclosure.Many variations and modifications may be made to the above-describedembodiments of the disclosure without departing substantially from thespirit and principles of the disclosure. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and protected by the following claims.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, or in computer software, firmware, or hardware, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. Embodiments ofthe subject matter described in this specification can be implemented asone or more computer program products, i.e., one or more modules ofcomputer program instructions encoded on a tangible program carrier forexecution by, or to control the operation of, data processing apparatus.The tangible program carrier can be a computer readable medium. Thecomputer readable medium can be a machine-readable storage device, amachine-readable storage substrate, a memory device, or a combination ofone or more of them.

The term “processor” encompasses all apparatus, devices, and machinesfor processing data, including by way of example a programmableprocessor, a computer, or multiple processors or computers. Theprocessor can include, in addition to hardware, code that creates anexecution environment for the computer program in question, e.g., codethat constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, or a combination of one or moreof them.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astandalone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program does notnecessarily correspond to a file in a file system. A program can bestored in a portion of a file that holds other programs or data (e.g.,one or more scripts stored in a markup language document), in a singlefile dedicated to the program in question, or in multiple coordinatedfiles (e.g., files that store one or more modules, sub programs, orportions of code). A computer program can be deployed to be executed onone computer or on multiple computers that are located at one site ordistributed across multiple sites and interconnected by a communicationnetwork.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., a field programmable gate array (FPGA) or anapplication specific integrated circuit (ASIC).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing instructions and one or more data memorydevices for storing instructions and data. Generally, a computer willalso include, or be operatively coupled to receive data from or transferdata to, or both, one or more mass storage devices for storing data,e.g., magnetic, magneto optical disks, or optical disks. However, acomputer need not have such devices.

Computer readable media suitable for storing computer programinstructions and data include all forms data memory includingnon-volatile memory, media and memory devices, including by way ofexample semiconductor memory devices, e.g., EPROM, EEPROM, and flashmemory devices; magnetic disks, e.g., internal hard disks or removabledisks; magneto optical disks; and CD ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

While this specification contains many specifics, these should not beconstrued as limitations on the scope of the claimed subject matter, butrather as descriptions of features that may be specific to particularembodiments. Certain features that are described in this specificationin the context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the embodiments described above should not be understoodas requiring such separation in all embodiments, and it should beunderstood that the described program components and systems cangenerally be integrated together in a single software product orpackaged into multiple software products.

While some embodiments of the present subject matter have beendescribed, it is to be understood that the embodiments described areillustrative only and that the scope of the invention is to be definedsolely by the appended claims when accorded a full range of equivalence,many variations and modifications naturally occurring to those of skillin the art from a perusal hereof.

We claim:
 1. A method for determining intermodulation distortion in acommunication system which operates using a predetermined set of radiofrequency (“RF”) channels and a predetermined signal type, the methodcomprising the steps of: (a) selecting a frequency bin; (b) generating acomplex envelope for a first signal in the frequency bin; (c)determining a cyclic autocorrelation function for the first signal; (d)comparing the determined cyclic autocorrelation function to a cyclicautocorrelation function for the predetermined signal type; and (e)comparing the frequency of the first signal with the frequency of thepredetermined set of RF channels.
 2. The method of claim 1 furthercomprising the step of: (f) determining a plurality of the RF channelsthat produced the first signal.
 3. The method of claim 2 furthercomprising the step of: (g) determining an intermodulation order foreach of the plurality of RF channels that produced the first signal. 4.The method of claim 1 wherein the frequency bin is selected based on apair of signals from the predetermined set of RF signals.
 5. The methodof claim 1 wherein step (d) includes determining if the first signalcomprises a predetermined characteristic of the predetermined signaltype.
 6. The method of claim 5 wherein the predetermined characteristicis selected from the group consisting of: cyclic prefix-inducedcyclostationarity, frame rate, and chip rate.
 7. The method of claim 1wherein at least one of the plurality of RF channels is selected fromthe group consisting of: a communication signal, an Orthogonal FrequencyDivision Multiplexed (“OFDM”) signal, and a Long Term Evolution (“LTE”)signal.
 8. The method of claim 1 wherein the first signal is not acommunication signal in the communication system.
 9. The method of claim1 wherein at least one of the plurality of RF channels is selected fromthe group consisting of: a tone, a modulated carrier, and noise.
 10. Asystem for determining intermodulation distortion in a communicationsystem which operates using a predetermined set of radio frequency(“RF”) channels and a predetermined signal type, comprising: a firstcircuit for selecting a frequency bin; a second circuit for generating acomplex envelope for a first signal in the frequency bin; a thirdcircuit for determining a cyclic autocorrelation function for the firstsignal; a first comparison circuit for comparing the determined cyclicautocorrelation function to acyclic autocorrelation function for thepredetermined signal type; and a second comparison circuit for comparingthe frequency of the first signal with the frequency of thepredetermined set of RF channels.
 11. The system of claim 10 furthercomprising a fourth circuit for determining a plurality of the RFchannels that produced the first signal.
 12. The system of claim 11further comprising a fifth circuit for determining an intermodulationorder for each of the plurality of RF channels that produced the firstsignal.
 13. The system of claim 11 wherein said first circuit selectssaid frequency bin based on a pair of signals from the predetermined setof RF signals.
 14. The system of claim 10 wherein said first comparisoncircuit includes circuitry for determining if the first signal comprisesa predetermined characteristic of the predetermined signal type.
 15. Thesystem of claim 10 wherein the predetermined characteristic is selectedfrom the group consisting of: cyclic prefix-induced cyclostationarity,frame rate, and chip rate.
 16. The system of claim 10 wherein at leastone of the plurality of RF channels is selected from the groupconsisting of: a communication signal, an Orthogonal Frequency DivisionMultiplexed (“OFDM”) signal, and a Long Term Evolution (“LTE”) signal.17. The system of claim 10 wherein the first signal is not acommunication signal in the communication system.
 18. The system ofclaim 10 wherein at least one of the plurality of RF channels isselected from the group consisting of: a tone, a modulated carrier, andnoise.
 19. A non-transitory machine-readable medium having storedthereon a plurality of executable instructions to be executed by aprocessor to implement a method of determining intermodulationdistortion in a communication system which operates using apredetermined set of radio frequency (“RF”) channels and a predeterminedsignal type, the method comprising the steps of: (a) selecting afrequency bin; (b) generating a complex envelope for a first signal inthe frequency bin; (c) determining a cyclic autocorrelation function forthe first signal; (d) comparing the determined cyclic autocorrelationfunction to a cyclic autocorrelation function for the predeterminedsignal type; and (e) comparing the frequency of the first signal withthe frequency of the predetermined set of RF channels.
 20. Thenon-transitory machine-readable medium of claim 19 wherein the methodimplemented further comprises the step of: (f) determining a pluralityof the RF channels that produced the first signal.
 21. Thenon-transitory machine-readable medium of claim 20 wherein the methodimplemented further comprises the step of: (g) determining anintermodulation order for each of the plurality of RF channels thatproduced the first signal.
 22. The non-transitory machine-readablemedium of claim 19 wherein the frequency bin is selected based on a pairof signals from the predetermined set of RF signals.
 23. Thenon-transitory machine-readable medium of claim 19 wherein step (d)includes determining if the first signal comprises a predeterminedcharacteristic of the predetermined signal type.
 24. The non-transitorymachine-readable medium of claim 23 wherein the predeterminedcharacteristic is selected from the group consisting of: cyclicprefix-induced cyclostationarity, frame rate, and chip rate.
 25. Thenon-transitory machine-readable medium of claim 19 wherein at least oneof the plurality of RF channels is selected from the group consistingof: a communication signal, an Orthogonal Frequency Division Multiplexed(“OFDM”) signal, and a Long Term Evolution (“LTE”) signal.
 26. Thenon-transitory machine-readable medium of claim 19 wherein the firstsignal is not a communication signal in the communication system. 27.The non-transitory machine-readable medium of claim 19 wherein at leastone of the plurality of RF channels is selected from the groupconsisting of: a tone, a modulated carrier, and noise.